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DECIMAL NUMBERS

DECIMAL NUMBERS. ALEXANDER PENUELA RAFAEL PEDRAZA RUIZ SANTIAGO HUERTAS SERGIO RIOS FELIPE BARCHA 4-A. PLACE VALUE. To understand decimal numbers you must first know about Place Value . When we write numbers, the position (or " place ") of each number is important. In the number 327:

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DECIMAL NUMBERS

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  1. DECIMAL NUMBERS ALEXANDER PENUELA RAFAEL PEDRAZA RUIZ SANTIAGO HUERTAS SERGIO RIOS FELIPE BARCHA 4-A

  2. PLACE VALUE To understand decimal numbers you must first know about Place Value. When we write numbers, the position (or "place") of each number is important. In the number 327: the "7" is in the Units position, meaning just 7 (or 7 "1"s), the "2" is in the Tens position meaning 2 tens (or twenty), and the "3" is in the Hundreds position, meaning 3 hundreds. "ThreeHundredTwentySeven"

  3. As we move left, each position is 10 times bigger! From Units, to Tens, to Hundreds ... and ... As we move right, each position is 10 times smaller. From Hundreds, to Tens, to Units But what if we continue past Units? What is 10 times smaller than Units? 1/10ths (Tenths) are!

  4. But we must first write a decimal point,so we know exactly where the Units position is: "three hundred twenty seven and four tenths" And that is a Decimal Number!

  5. Decimal numbers The zero and the counting numbers (1,2,3,...) make up the set of whole numbers. But not every number is a whole number. Our decimal system lets us write numbers of all types and sizes, using a clever symbol called the decimal point. As you move right from the decimal point, each place value is divided by 10. decimal point 1 2 7 . 8 5 4 Hundreds tens hundredths ones tenths thousandths

  6. MODELING DECIMALS The decimal number can be represented by square or large rectangles. 3 10 0.3 =

  7. TYPES OF DECIMAL NUMBER There are three different types of decimal number: exact, recurring and other decimals. An exact or terminating decimal is one which does not go on forever, so you can write down all its digits. For example: 0.125 A recurring decimal is a decimal number which does go on forever, but where some of the digits are repeated over and over again. For example: 0.1252525252525252525... is a recurring decimal, where '25' is repeated forever. Other decimals are those which go on forever and don't have digits which repeat. For example pi = 3.141592653589793238462643...

  8. PROBLEM SOLVING Example 1: If 58 out of 100 students in a school are boys, then write a decimal for the part of the school that consists of boys. Analysis: We can write a fraction and a decimal for the part of the school that consists of boys Answer: 0.58

  9. Step 2: The least decimal is 9.75. Now we must determine how 9.75 compares with the winning score. Answer: The last swimmer must get a score less than 9.75 s in order to win. Step 1: 9 . 75 9 . 79 9 . 80 9 . 81

  10. Example 3: Ellen wanted to buy the following items: A DVD player for $49.95, a DVD holder for $19.95 and a personal stereo for $21.95. Does Ellen have enough money to buy all three items if she has $90 with her? Analysis: The phrase enough money tells us that we need to estimate the sum of the three items. We will estimate the sum by rounding each decimal to the nearest one. We must then compare our estimated sum with $90 to see if she has enough money to buy these items. $50.00 $20.00 $22.00 $92.00 $49.95 $19.95 $21.95 Answer: No, because rounding each decimal to the nearest one, we get an estimate of $92, and Ellen only has $90 with her.

  11. EXAMPLES FOR THE REAL LIFE (1) In the 1968 SummerOlympics, IrenaSzewinska of Poland won thewomen´s 200 metersdashwith a time of 22.5 seconds,. In 1996, Marie-JosePerec of France won theeventwith a time of 22.12 seconds. Whose time isfaster?

  12. EXAMPLES FOR THE REAL LIFE (1) Thetens´andones´digits are thesame. Write a zero as a placeholder. 22.50 22.12 Thetenths´digits are different. 5 > 1, so 22.50 > 22.12 Answer: Because 22.5 > 22.12, Perec´s time is faster

  13. EXAMPLES FOR THE REAL LIFE (2) Central Park, in Manhattan, New York, isone of theworld´smostfamousparks. Ifyouwalkedaroundtheentireperimeter of the 2.5 mileby 0.5 milepark, howfarwouldyouwalk?

  14. EXAMPLES FOR THE REAL LIFE (2) 0.5 mile wide 2.5 milelong Solution: A = lw Write formula for area of = 2.5 (0.5) Substitute 2.5 for l and 0.5 for w. = 1.25 Multiply. Answer: The area of Central Park is about 1.25 square miles.

  15. EXAMPLES FOR THE REAL LIFE (3) Ticket prices:Thecost of 21 tickets tosee Blue ManGroupis $761.25 . Howmuchdoeseach ticket? You can use longdivisionto divide a decimal by a wholenumber. Divide as withwholenumbers. Then line up the decimal points in thequotient and thedividend.

  16. EXAMPLES FOR THE REAL LIFE (3) Solution: Dividing a decimal by a Whole Number 36.25 21 ) 761.25 63 131 126 52 42 105 105 0 Answer: Each ticket costs $36.25

  17. EXAMPLES FOR THE REAL LIFE (4) LongestSubmarineSandwich: In 1979, Chef Franz Eichenauermade a submarinesandwichthatwas 322.5 meterslong. Supposethesandwichwascutintopieceseachmeasured 25.8 centimeters. Howmanywouldtherebe?

  18. EXAMPLES FOR THE REAL LIFE (4) Solution: 1. Convert 322.5 meters to centimeters by multipliying by 100. 322.5 x 100 = 32,250 so 322.5 m = 32,250 cm 2. To find the number of pieces, divide the total length of the sandwich by the length of each piece. 32,250 cm ÷ 25.8 cm = 1.250 Answer: The submarine sandwich would be divided into 1.250 pieces.

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